How many solutions does the system of linear equations have ? Y=3/4x+12

Present age of Selma = s

Present age of Joyce = j

Selma is now 3 times as old as joyce

s=3j........(1)

Four years ago,

s-4=j-4

then

Selma was 4 times as old as joyce

s-4=4(j-4)

s-4=4j-16

s=4j-16+4

s=4j-12.............(2)

Put the value of s in (2) from (1)

3j=4j-12

3j-4j=-12

-j=-12

Multiply by -1 both sides

j=12

Put the value of j in (1)

s=3j

s=3(12)

s=36

Present age of Selma = s = 36 years old

Present age of Joyce = j = 12 years old

Answer:

21 inches

Step-by-step explanation:

May had just over 6 inches of rain, June had just about 9 inches of rain, and July had just under 6 inches of rain. Together, these months had 9 + 6 + 6 = 21 inches of rain.

Answer:

x = 2

Step-by-step explanation:

The volume of this prism is half the volume of it as a rectangular prism. The volume is listed as 30. The rectangular prism would be 60. Volume is found by multipyling base, height and width.

The base is 10 and the width is 3.

Divide 60 by 10 and by 3.

60/10 = 6

6/3 = 2

This means the height x is 2.

There are 20 male students.

Hope this helps.

[tex]36 \times r = 21 \times 12 \\ 36r = 252 \\ r = 252 \div36 \\ r = 7[/tex]

The question asks to solve a proportion 36/42 = 24/r. By cross-multiplication and solving the resulting equation for r, it is found that r = 28. Therefore, the correct value of r in this instance is 28.

To solve the mathematical problem 36/42 = 24/r for the value of r, you should cross-multiply and then solve for r. Cross-multiplication means you multiply 36 by r and 42 by 24, which results in the equation 36r = 42 * 24. When you divide both sides by 36, you get r = 42 * 24 / 36 as the final form of the equation. After calculating the products and divison, you will find that r = 28.

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Enlargement

Hope this helps :)

Answer:

Yes; there is only one range value for each domain value

Step-by-step explanation:

A relation can be defined as a function f(x) if for each value of the domain of x, there exists a unique value of f(x).

For example

(2, 4)(3, 9)(-2, 4)(4, 16) Is a Function

(2, 4)(2,6)(3, 8)(3, -8) Is Not a Function

To analyze if the relationship shown is a function, you must observe that each value of the domain has a single value of the range assigned.

For the given points {(-5, 6), (-2, 3), (3, 2), (6, 4)} this requirement is satisfied. Therefore, the relationship is a function. The graph is shown in the attached image.

The correct option is: Yes; there is only one range value for each domain value

Answer:

Yes; there is only one range value for each domain value.

Step-by-step explanation:

Let, R = {(-5, 6), (-2, 3), (3, 2), (6, 4)} is a relation,

Since, a relation is called a function if there is only one output value for each input value,

Here, the image of -5 is 6,

Image of -2 is 3,

Image of 3 is 2,

Image of 6 is 4,

That is, there is only one output value for each distinct input value,

Thus, R is a function,

Now, the input value is called domain value and output value is called range value,

Hence, SECOND OPTION is correct.

Answer:

= -7

Step-by-step explanation:

6 ⁹ ×6^x = 6²

From the laws of indices;

aⁿ × aⁿ = a^2n

Therefore;

6 ⁹ ×6^x = 6^(9+x)

6^(9+x) = 6²,

Since the bases are the same then the exponents are equal;

9+x = 2

x = -7

Answer:

x=-7

Step-by-step explanation:

[tex]6^9 \cdot 6^x = 6^2[/tex]

Apply exponential property to solve for x

[tex]a^m \cdot a^n = a^{m+n}[/tex]

[tex]6^9 \cdot 6^x = 6^{9+x}[/tex]

So the given equation becomes

[tex]6^{9+x}= 6^2[/tex]

Both sides of the equation has same base 6

So we equate the exponent and solve for x

[tex]9+x= 2[/tex]

Subtract 9 from both sides

[tex]x=-7[/tex]

Answer:

x = 9

Step-by-step explanation:

Given that,

coordinate 1  = (-6,10)

coordinate 2 = (12,-2)

Find the slope of line which contain above coordinates

Formula to use

[tex]m=\frac{y2 - y1}{x2-x1}[/tex]

m = [tex]\frac{-2-10}{12+6}[/tex]

m  = -2/3

Find the equation of the line

Formula to use

y = mx + c

where m is the slope =  -2/3

           c is the y intercept

Using coordinate (-6,10)

Plug in the formula

10 = -2/3(-6) + c

10 = 4 + c

c = 10-4

c = 6

So, the equation will be

y = -2/3x + 6

Find the x-intercept

we know that the x-intercept is the value of x when the value of y is equal to zero

so substitute y with 0 in the equation

when y = 0

0 = -2/3x + 6

2/3x = 6

x = 6(3/2)

x = 9

Answer:

x = 9 is the x-intercept.

Step-by-step explanation:

We have given the coordinates (-6,10) and (12,-2).

We have to find the  x-intercept of the line containing these points.

First we find the slope m by using these points.

We know that m = (y₂-y₁)/(x₂-x₁)

m = -2/3

The general form of the equation of line is :

y = mx + c

Where c is the y intercept.

Using the first coordinate to find c .

10 = (-2/3)(-6) +c

c = 6

So, the required equation is :

y = (-2/3)x+6

We have to find the x-intercept.

For this we put y=0

(-2/3)x+6 = 0

2/3 x = 6

x  = 6(3/2)

x = 9 is the x-intercept.

Answer:

0.4

Step-by-step explanation:

0.4 as a percentage is 40%

25% is obviously 25%

10 is also obviously 10%

Answer:

Step-by-step explanation:

General Solution

Left hand side

tan(30) + 1 / tan(30

tan^2(30) + 1

============

tan 30

but tan^2(30) + 1 = sec^2(30)

sec^2(theta) / tan(30) Let theta = 30o. This will work for any angle between 0 and 90

[tex]\dfrac{sec^2(theta)}{tan(theta)} = \dfrac{sec^2(theta)}{\dfrac{sin(theta)}{cos(theta)}} = \dfrac{1}{\dfrac{cos^2(theta)*sin(theta)}{cos(theta)}}[/tex]

Cancel out cos(theta) and one of cos^2(theta)

leaving your with

[tex]\dfrac{1}{sin(theta)*cos(theta)}[/tex]

which is exactly what the right hand side is.

This is the way this problem should be done. If you want to show what happens with 30o then

Thirty degree angle

tan(30) = 0.5774

Left hand side

0.5774 + 1/(0.5774) = 2.3093

Right hand side

1/(sin(30)*cos(30))

1/(0.5 * 0.8660)

1/(0.4330

2.3094

Which is about as close as you will get when you round.

14 = 2y/5 | *5

70 = 2y | :2

35 = y

Test :

14 = 2*35/5 TRUE

Answer:

y=35

Step-by-step explanation:

[tex]\frac{2y}{5}=14\\2y=14*5\\2y=70\\y=\frac{70}{2}\\y=35\\\\Checking\\\frac{2(35)}{5} \\\frac{70}{5} \\=14[/tex]

2/x-9

is the answer to this problem

Answer:

2/x−9

Step-by-step explanation:

Write it out just the way you read it, then follow the order of operations.

The “Order of Operations” (P-E-MD-AS … or … B-O-DM-AS) tells us that quotient (division) comes before less (subtraction) so:

How do you represent “the quotient of two and (a number) X” ?

The quotient of 2 divided by X is (2÷X) or (2/X) or 2

What is nine less than that quotient?

subtract 9 from your choice of the previous representations, for example:

2/x−9

Answer:

[tex]y^2=-8x[/tex]

Step-by-step explanation:

The directrix intersects the x-axis at point (2,0). Points (-2,0) and (2,0) are symmetric about the origin, so the vertex of the parabola is placed at the origin (0,0).

The parameter p of the parabola is the distance from the focus to the directrix, thus p=4.

The branches of the parabola go in negative direction of x-axis, because the focus lies to the left from the vertex.

The equation of the parabola is

[tex](y-0)^2=-2\cdot 4\cdot (x-0),\\ \\y^2=-8x.[/tex]

Answer:

a = 9.632  and b is 10

9.632*10^10 in^3  scientific form

96,320,000,000   in^3  standard form

Step-by-step explanation:

To find volume of a rectangular prism

V = l*w*h

   = 1.4 * 10^4   ( 4.3 * 10^3)   (1.6* 10^3)

When multiply powers of 10, we multiply the numbers out front

1.4*4.3*1.6 =9.632

Then we add the powers of 10

10^(4+3+3)

10^10

The volume is 9.632*10^10 in^3

a = 9.632  and b is 10

In standard form we move the decimal 10 places to the right.  If there are not enough numbers we add zeros

9.632*10^10 in^3

96,320,000,000   in^3

Answer: The answer is 90.

Step-by-step explanation:

Answer:

30 ft^2

Step-by-step explanation:

Area of square = 12 x 12 = 144

Area of circle = 3.14 x 6^3 = 3.14 x 36 = 113.04

So area of the remaining board = 144 - 113.04 = 30.96

Answer: 30 ft^2

The Answer Is J.14.50

Answer: $14.50

Step-by-step explanation:

Multiply $5.95 by 2.

Multiply $0.65 by 4.

Add both of the answers to the multiplying problems

Your final answer... I hope I was able to help!

Answer:

C

Step-by-step explanation:

The sum to infinity of a geometric series is

[tex]\frac{a_{1} }{1-r}[/tex] ( - 1 < r < 1 ) ← substitute values

S( ∞ ) = [tex]\frac{5}{1-\frac{1}{3} }[/tex] = [tex]\frac{5}{\frac{2}{3} }[/tex] = [tex]\frac{15}{2}[/tex]

The sum of the infinite geometric series is [tex]\frac{15}{2}[/tex]

The sum of all the terms of a geometric sequence is called infinite geometric series.

If a, ar, a[tex]r^{2}[/tex], ...., a[tex]r^{n-1}[/tex], .... is a geometric series, then  a+ar+a[tex]r^{2}[/tex]+ ....+a[tex]r^{n-1}[/tex]+.... is the corresponding infinite geometric series.

where a is the 1st term & r is the common ratio between consecutive terms of the series.

Sum of infinite geometric series = [tex]\frac{a}{1-r}[/tex] ; |r|<1

Given, 1st term ([tex]a_{1}[/tex]) of the infinite geometric series = 5

Common ratio (r) = 1/3

∴ Sum of infinite geometric series = [tex]\frac{a_{1} }{1-r}[/tex]

                                                         = [tex]\frac{5}{1-\frac{1}{3} }[/tex]

                                                         = [tex]\frac{5}{\frac{2}{3} }[/tex]

                                                         = [tex]\frac{15}{2}[/tex]

Learn more about geometric series here :

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Answer:

x would equal -4

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Count how many l's there are, how many h's there are, and how many w's there are.

Answer:

[tex]\large\boxed{B.\ S.A.=2lw+2lh+2wh}[/tex]

Step-by-step explanation:

It's the net of a rectangular prism.

The formula of a surfave area of a rectangular prism:

[tex]S.A.=2lw+2lh+2wh[/tex]

We have two rectangles l × w, two rectangles l × h and two rectangles w × h.

Answer:

(a - 7)(3 - x)

Step-by-step explanation:

Given

3(a - 7) - x(a - 7) ← factor out (a - 7) from both terms

= (a - 7)(3 - x)

Answer:

3 1/6

Step-by-step explanation:

To find the highest value, we have to evaluate each term individually,

1)  1 1/6 = 7/6 = 1.167

2) 3 1/6 = 19/6 = 3.16

3) 3/8 = 0.375

4) 5/8 = 0.625

Therefore, second data value (3 1/6) is highest.

200,000/52 weeks in a year =$3846.153846 each week

Her weekly paycheck is 3835.82

As we know that there are 52.14 weeks in a year

So weekly paycheck will be 200,000 / 52.14 = 3835.82

Since she gets weekly check so her weekly paycheck is 3835.82

The subject of this question is Mathematics.

As a tutor, I would need more information about the specific question or problem you are working on to provide a detailed answer. Mathematics encompasses a wide range of topics including algebra, geometry, statistics, and calculus, among others. If you can provide more details about the specific topic or concept you are struggling with, I can provide a step-by-step explanation to help you understand.

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Answer:

I think its 14. If not, check other options. Bye!

Step-by-step explanation:

The estimated length of a paperback book is "8 inches".

The paperback also called a paperback or softback, is a sort of book with a thick paper or paperboard cover that is often held together along with glue rather than stitches or staples.

Hardcover or hardcover books, but at the other extreme, are bonded with cardboard covered in linen, plastic, or leather.

Since 4 inches is far too short, and "14 and 18 " inches is longer than a ruler.

Therefore, the answer is "8 inches".

Find out more information about the book here:

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Answer:

Option B.

Step-by-step explanation:

Let

s-----> the number of songs that Eva downloaded

we know that

The linear equation that represent the situation is

[tex]1.29s=11.61[/tex]

Solve for s

Divide by 1.29 both sides

[tex]s=11.61/1.29[/tex]

[tex]s=9\ songs[/tex]

therefore

Ari's work is correct

Answer:

answer b

Step-by-step explanation:

i took test

Answer:

122

Step-by-step explanation:

34 + 84 = 122

Answer:

D.

Step-by-step explanation:

A is linear, you can figure out that y=x+5

B is linear, y=22(x+1)

C is linear, y=8x+5

D is exponential, y=3ˣ⁺¹

Deriving these formulas is a matter of trial and error if you know you can choose between linear and exponential.

If your taking about question three, the answer would be B.) because an exponent added to a number is basically the number multiplied by itself by them number amount in the exponent(example: 5 to the power of 2 would be 5x5).

Answer:

Step-by-step explanation:

It's geometric.

You are starting with -2 and multiplying each successive term by - 2

r = - 2

a1 = -2

tn = ar^(n - 1)

So to try it out, let n be the 4th term

t4 = -2 * (-2)^(4 - 1)

t4 = - 2 * (-2)^3

t4 = - 2 * -8

t4 = 16 just as the series indicated.